Complex Numbers 1

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Mark Hodds

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Mark Hodds 8 years, 5 months ago

Created this as a copy of The modulus of complex numbers.

Name	Status	Author	Last Modified
The modulus of complex numbers	Has some problems	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Complex Numbers 1	draft	Mark Hodds	13/11/2016 19:37

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Question statement

Find the modulus of each of the following complex numbers, leaving your answer in decimal form to 3 decimal places:

Give any introductory information the student needs.

			Name	Type	Generated Value

ans1	number	9.220
ans2	number	43.863
ans3	number	55.902
ans4	number	0.950
b4	integer	8
b1	integer	7
b2	integer	7
b3	integer	1
d4	integer	6
d2	integer	5
s8	integer	1
s3	integer	-1
s2	integer	1
s1	integer	1
s7	integer	1
s6	integer	-1
s5	integer	1
s4	integer	1
z2	number	5 + 7i
tol	number	0.001
c4	integer	6
a1	integer	6
a3	integer	-2
a2	integer	5
a4	integer	1
z4	number	-2 + i
z5	number	1 + 8i
z6	number	6 + 6i
z1	number	6 + 7i
c2	integer	-1
z3	number	-1 + 5i
f	integer	6
n	integer	5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
precround(abs(z1),3)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `number`

9.220

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
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Part b) Gap-fill
1. Gap Number entry
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Part c) Gap-fill
1. Gap Number entry
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Part d) Gap-fill
1. Gap Number entry
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$|\var{z1}|=\;\;$ Unnamed gap

Advice

Recall that $|a+bi|=\sqrt{a^2+b^2}$ and that:

1. $|z^n| = |z|^n$

2. $|z_1z_2|=|z_1|\;|z_2|$

3. $|z_1/z_2|=|z_1|/|z_2|$

$\begin{eqnarray*} |\var{z1}|&=&\sqrt{(\var{a1})^2+(\var{b1})^2}\\ &=& \var{abs(z1)}\\ &=&\var{ans1} \end{eqnarray*}$ to 3 decimal places.

$\begin{eqnarray*} |(\var{z2})(\var{z3})|&=&|\var{z2}|\;|\var{z3}|\\ &=& \var{abs(z2)}\times \var{abs(z3)}\\ &=&\var{abs(z2*z3)}\\ &=&\var{ans2} \end{eqnarray*}$ to 3 decimal places.

$\begin{eqnarray*} |(\var{z4})^{\var{n}}|&=&|\var{z4}|^{\var{n}}\\ &=& \var{abs(z4)}^{\var{n}}\\ &=& \var{abs(z4)^n}\\ &=&\var{ans3} \end{eqnarray*}$ to 3 decimal places.

$\begin{eqnarray*} \left|\frac{\var{z5}}{\var{z6}}\right|&=&\frac{|\var{z5}|}{|\var{z6}|}\\ &=& \frac{\var{abs(z5)}}{\var{abs(z6)}}\\ &=& \var{abs(z5/z6)}\\ &=&\var{ans4} \end{eqnarray*}$ to 3 decimal places.

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This question is used in the following exam:

101MP 2019 - Complex Numbers Week 8 by Mark Hodds in 101MP 2018.

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Taxonomy: mathcentre

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Mark Hodds 8 years, 5 months ago

Error in variable testing condition

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Generated value: `number`

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Complex Numbers 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Mark Hodds 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`